Yes, it is a Zumo issue because it does not implement AD2P as a receiver.
Read about it here: http://en.wikipedia.org/wiki/Bluetooth
Although I may not have it exactly right, this should help you understand why.
BT uses a "profile" to define the protocol between two devices. Your Droid connects to the Zumo using the Hands Free Profile (HFP). Your phone does not usually transmit music using that profile, so the zumo will never get to process the music. You might be able to find a music app that can do this, but it would be monaural and you wouldn't have AVRCP (the ability to pause/skip/etc).
Ideally, the Zumo would be both the receiver and transmitter of AD2P (stereo music) and AVRCP. This would allow it to receive the stereo music from your phone and re-transmit it to your headset (or wired earphones). Unfortunately the Zumo 550 is not designed to work this way (I don't know if the 660/665 is).